Bimodal Behavior and Convergence Requirement in Macroscopic Properties of the Multiphase Interstellar Medium Formed by Atomic Converging Flows

We systematically perform hydrodynamics simulations of 20 $\mathrm{km}\,{{\rm{s}}}^{-1}$ converging flows of the warm neutral medium (WNM) to calculate the formation of the cold neutral medium (CNM), focusing especially on the mean properties of the multiphase interstellar medium (ISM), such as the mean density on a 10 pc scale. Our results show that convergence in those mean properties requires a 0.02 pc spatial resolution that resolves the cooling length of the thermally unstable neutral medium (UNM) to follow the dynamical condensation from the WNM to the CNM. We also find that two distinct postshock states appear in the mean properties depending on the amplitude of the upstream WNM density fluctuation ${\rm{\Delta }}{\rho }_{0}$ ( $=\,\sqrt{\langle \delta {\rho }_{0}^{2}\rangle }{/\rho }_{0}$ ). When ${\rm{\Delta }}{\rho }_{0}\gt 10 \% $ , the interaction between shocks and density inhomogeneity leads to a strong driving of the postshock turbulence of >3 km s^-1, which dominates the energy budget in the shock-compressed layer. The turbulence prevents dynamical condensation by cooling, and the CNM mass fraction remains at ∼45%. In contrast, when ${\rm{\Delta }}{\rho }_{0}\leqslant 10 \% $ , the CNM formation proceeds efficiently, resulting in the CNM mass fraction of ∼70%. The velocity dispersion is limited to the thermal-instability-mediated level of ∼2-3 km s^-1, and the layer is supported by both turbulent and thermal energy equally. We also propose an effective equation of state that models the multiphase ISM formed by the WNM converging flow as a one-phase ISM in the form of P ∝ ρ^γ_eff, where γ_eff varies from 0.9 (for a large pre-shock Δρ₀) to 0.7 (for a small pre-shock Δρ₀).